Discrete time LPV I/O and state space representations, differences of behavior and pitfalls of interpolation

A common approach for modeling LPV systems is to interpolate between local LTI models, often obtained by system identification methods. We study the results of interpolating in different domains, the so called I/O domain and the state-space domain. It is shown that significant differences can occur between the interpolated models, due to differences in time propagation of the (scheduling) parameter. We introduce canonical representations for LPV state-space realizations similar to the LTV framework and derive exact formulas for the connection between I/O and state-space based LPV models.